The advent of Pendulum Summoning may help them to swarm the Field quickly (except for "Hazy Flame Peryton", that has a Special Summon restriction), allowing the player to Summon up to 5 "Hazy Flame" monsters at once and have quick access to Xyz Summons.

Some other cards that can help a "Hazy Flame" deck include:

"Hieratic Dragon of Tefnuit": you can Special Summon it and then tribute it in order to Normal Summon a "Hazy Flame" monster; use its effect to Special Summon "Tyhone #2". With this, it is already possible to Xyz Summon "Basiltrice", but if you Tribute Summon "Hazy Flame Peryton", you can use its effect to Special Summon 2 "Hazy Flame Hydras" from your deck and add 2 more "Hazy Flame" fallen monsters as Xyz Materials to it.

"Card Advance": use it in order to be aware of the top cards of your deck and use the effect of "Hazy Flame Sphynx" at its best; it also gives you an additional Tribute Summon.

"Flamvell Firedog": it can be used to Special Summon "Hazy Flame Cerbereus" from your Deck, which will have its solid 2000 ATK intact.

"Onslaught of the Fire Kings": can also be used to Special Summon "Cerbereus" while allowing you to use its searching effect during the End Phase.

"Fairy Knight Ingunar": you can bounce every other card on the Field to the hand and can refuel its effect by using "Hazy Pillar".

"Stoic Challenge": if you equip a 5-Xyz Material "Basiltrice" with this card, it will gain a massive 3000 ATK boost, double the Battle Damage dealt to an opponent's monster and will not be destroyed during your opponent's End Phase.

"Vanity's Emptiness": once you have a 5-Xyz Material "Basiltrice" out, this card can help you maintain the control of the game by preventing your opponent from Special Summoning potentially dangerous monsters.

Volcanic Shell: once in the graveyard, it can search copies of itself from the deck for 500 Lps, allowing you to use the effect of Peryton a few times without losing hand advantage.

Weaknesses

Due to the variety of abilities, immunity against targeting effects and the fact that the main objective is to Xyz Summon Rank 6 monsters, virtually there is not a wide range of options of cards that can totally shut a "Hazy Flame" deck down. However, cards that forbids or restrict Special Summons, such as "Vanity's Emptiness", "El Shaddoll Winda" etc., can prevent them from swarming the Field. Restrictions towards their Level or Attribute, such as "Tualatin" and "Stygian Dirge" can also mean trouble to a dedicated "Hazy Flame" deck. If a player Xyz Summons "Basiltrice" with 3 or less Xyz Materials, it is also vulnerable to "Xyz Encore", "Compulsory Evacuation Device", etc; once their strategy of swarming the Field in order to Summon their ace monster is costly (i.e. "Peryton" must send itself and another FIRE monster to the Graveyard to Special Summon 2 monsters; "Sphynx" mills the top card of the Deck), losing that Xyz Monster right off the bat would be a heavy punishment in terms of card advantage, rendering the player probably out of resources; simply negating the Xyz Summon also works.